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PubMed1990

Uncertainties in pharmacokinetic modeling for perchloroethylene. I. Comparison of model structure, parameters, and predictions for low-dose metabolism rates for models derived by different authors.

In recent years physiologically based pharmacokinetic models have come to play an increasingly important role in risk assessment for carcinogens. The hope is that they can help open the black box between external exposure and carcinogenic effects to experimental observations, and improve both high-dose to low-dose and interspecies projections of risk. However, to date, there have been only relatively preliminary efforts to assess the uncertainties in current modeling results. In this paper we compare the physiologically based pharmacokinetic models (and model predictions of risk-related overall metabolism) that have been produced by seven different sets of authors for perchloroethylene (tetrachloroethylene). The most striking conclusion from the data is that most of the differences in risk-related model predictions are attributable to the choice of the data sets used for calibrating the metabolic parameters. Second, it is clear that the bottom-line differences among the model predictions are appreciable. Overall, the ratios of low-dose human to bioassay rodent metabolism spanned a 30-fold range for the six available human/rat comparisons, and the seven predicted ratios of low-dose human to bioassay mouse metabolism spanned a 13-fold range. (The greater range for the rat/human comparison is attributable to a structural assumption by one author group of competing linear and saturable pathways, and their conclusion that the dangerous saturable pathway constitutes a minor fraction of metabolism in rats.) It is clear that there are a number of opportunities for modelers to make different choices of model structure, interpretive assumptions, and calibrating data in the process of constructing pharmacokinetic models for use in estimating "delivered" or "biologically effective" dose for carcinogenesis risk assessments. We believe that in presenting the results of such modeling studies, it is important for researchers to explore the results of alternative, reasonably likely approaches for interpreting the available data--and either show that any conclusions they make are relatively insensitive to particular interpretive choices, or to acknowledge the differences in conclusions that would result from plausible alternative views of the world.

Animals↗
PubMed2003

Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil.

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

Aedes↗
PubMed2004

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model.

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.

Animals↗
PubMed2005

Multiple imputation under Bayesianly smoothed pattern-mixture models for non-ignorable drop-out.

Conventional pattern-mixture models can be highly sensitive to model misspecification. In many longitudinal studies, where the nature of the drop-out and the form of the population model are unknown, interval estimates from any single pattern-mixture model may suffer from undercoverage, because uncertainty about model misspecification is not taken into account. In this article, a new class of Bayesian random coefficient pattern-mixture models is developed to address potentially non-ignorable drop-out. Instead of imposing hard equality constraints to overcome inherent inestimability problems in pattern-mixture models, we propose to smooth the polynomial coefficient estimates across patterns using a hierarchical Bayesian model that allows random variation across groups. Using real and simulated data, we show that multiple imputation under a three-level linear mixed-effects model which accommodates a random level due to drop-out groups can be an effective method to deal with non-ignorable drop-out by allowing model uncertainty to be incorporated into the imputation process.

Antipsychotic Agents↗
PubMed2001

Health status and healthy life measures for population health need assessment: modelling variability and uncertainty.

It is increasingly recognised that population health need assessments based on the comparison of clinical or demographic end points (e.g. area mortality rates) neglect population variation in broader aspects of health status and health-related quality of life. Similarly, outcome measures which neglect impacts on health-related quality of life may be an inadequate basis for assessing the effectiveness of health interventions. This paper reviews issues in assessing needs and outcomes at population level based on health status valuations. It considers especially the modelling of sources of uncertainty in measures of health status by using Bayesian sampling estimation methods which produce a distribution of summary outcome measures. The modelling issues are illustrated in models for individual level health status from survey responses and their incorporation in area life tables to derive total and healthy life expectancies. In particular, a health status index derived from Short Form 36 profile responses in a health and lifestyle survey in a London health authority provides a case study of community health needs assessment.

Adolescent↗
PubMed2001

Uncertainties in model-based outcome predictions for treatment planning.

PURPOSE: Model-based treatment-plan-specific outcome predictions (such as normal tissue complication probability [NTCP] or the relative reduction in salivary function) are typically presented without reference to underlying uncertainties. We provide a method to assess the reliability of treatment-plan-specific dose-volume outcome model predictions. METHODS AND MATERIALS: A practical method is proposed for evaluating model prediction based on the original input data together with bootstrap-based estimates of parameter uncertainties. The general framework is applicable to continuous variable predictions (e.g., prediction of long-term salivary function) and dichotomous variable predictions (e.g., tumor control probability [TCP] or NTCP). Using bootstrap resampling, a histogram of the likelihood of alternative parameter values is generated. For a given patient and treatment plan we generate a histogram of alternative model results by computing the model predicted outcome for each parameter set in the bootstrap list. Residual uncertainty ("noise") is accounted for by adding a random component to the computed outcome values. The residual noise distribution is estimated from the original fit between model predictions and patient data. RESULTS: The method is demonstrated using a continuous-endpoint model to predict long-term salivary function for head-and-neck cancer patients. Histograms represent the probabilities for the level of posttreatment salivary function based on the input clinical data, the salivary function model, and the three-dimensional dose distribution. For some patients there is significant uncertainty in the prediction of xerostomia, whereas for other patients the predictions are expected to be more reliable. In contrast, TCP and NTCP endpoints are dichotomous, and parameter uncertainties should be folded directly into the estimated probabilities, thereby improving the accuracy of the estimates. Using bootstrap parameter estimates, competing treatment plans can be ranked based on the probability that one plan is superior to another. Thus, reliability of plan ranking could also be assessed. CONCLUSIONS: A comprehensive framework for incorporating uncertainties into treatment-plan-specific outcome predictions is described. Uncertainty histograms for continuous variable endpoint models provide a straightforward method for visual review of the reliability of outcome predictions for each treatment plan.

Humans↗
PubMed2001

Uncertainty management in integrated assessment modeling: towards a pluralistic approach.

Integrated Assessment (IA) is an evolving research community that aims to address complex societal issues through an interdisciplinary process. The most-widely used method in Integrated Assessment is modeling. The state of the art in Integrated Assessment modeling is described in this paper in terms of history, general features, classes of models, and in terms of the strengths and weaknesses, and the dilemmas and challenges modelers face. One of the key challenges is the issue of uncertainty management. The paper outlines the sources and types of uncertainty modelers are confronted with. It then discusses how uncertainties are currently managed in Integrated Assessment modeling, on which evaluation it is argued that complementary methods are needed that allow for pluralistic uncertainty management. The paper finalises with discussing pluralistic concepts and approaches that are currently explored in the IA community and that seem promising in view of the challenge to incorporate explicitly more than one hidden perspective in models.

Animals↗
PubMed2005

Local and global uncertainty analyses of a methane flame model.

Local and global uncertainty analyses of a flat, premixed, stationary, laminar methane flame model were carried out using the Leeds methane oxidation mechanism at lean (phi = 0.70), stoichiometric (phi = 1.00), and rich (phi = 1.20) equivalence ratios. Uncertainties of laminar flame velocity, maximal flame temperature, and maximal concentrations of radicals H, O, OH, CH, and CH(2) were investigated. Global uncertainty analysis methods included the Morris method, the Monte Carlo analysis with Latin hypercube sampling, and an improved version of the Sobol' method. Assumed probability density functions (pdf's) were assigned to the rate coefficients of all the 175 reactions and to the enthalpies of formation of the 37 species. The analyses provided the following answers: approximate pdf's and standard deviations of the model results, minimum and maximum values of the results at any physically realistic parameter combination, and the contribution of the uncertainty of each parameter to the uncertainty of the model result. The uncertainty of a few rate parameters and a few enthalpies of formation causes most of the uncertainty of the model results. Most uncertainty comes from the inappropriate knowledge of kinetic data, but the uncertainty caused by thermodynamic data is also significant.

Journal Article↗
PubMed2006

Application of knowledge-driven spatial modelling approaches and uncertainty management to a study of Rift Valley fever in Africa.

BACKGROUND: There are few studies that have investigated uncertainties surrounding the scientific community's knowledge of the geographical distribution of major animal diseases. This is particularly relevant to Rift Valley fever (RVF), a zoonotic disease causing destructive outbreaks in livestock and man, as the geographical range of the disease is widening to involve previously unaffected regions. In the current study we investigate the application of methods developed in the decision sciences: multiple criteria decision making using weighted linear combination and ordered weighted averages, and Dempster-Shafer theory, implemented within the geographical information system IDRISI, to obtain a greater understanding of uncertainty related to the geographical distribution of RVF. The focus is on presenting alternate methods where extensive field data are not available and traditional, model-based approaches to disease mapping are impossible to conduct. RESULTS: Using a compensatory multiple criteria decision making model based on weighted linear combination, most of sub-Saharan Africa was suitable for endemic circulation of RVF. In contrast, areas where rivers and lakes traversed semi-arid regions, such as those bordering the Sahara, were highly suitable for RVF epidemics and wet, tropical areas of central Africa had low suitability. Using a moderately non-compensatory model based on ordered weighted averages, the areas considered suitable for endemic and epidemic RVF were more restricted. Varying the relative weights of the different factors in the models did not affect suitability estimates to a large degree, but variations in model structure had a large impact on our suitability estimates. Our Dempster-Shafer analysis supported the belief that a range of semi-arid areas were suitable for RVF epidemics and the plausibility that many other areas of the continent were suitable. Areas where high levels of uncertainty were highlighted included the Ethiopian Highlands, southwest Kenya and parts of West Africa. CONCLUSION: We have demonstrated the potential of methods developed in the decision sciences to improve our understanding of uncertainties surrounding the geographical distribution of animal diseases, particularly where information is sparse, and encourage wider application of the decision science methodology in the field of animal health.

Africa South of the Sahara↗
PubMed2003

Correlations between parameters in risk models: estimation and propagation of uncertainty by Markov Chain Monte Carlo.

Monte Carlo simulation has become the accepted method for propagating parameter uncertainty through risk models. It is widely appreciated, however, that correlations between input variables must be taken into account if models are to deliver correct assessments of uncertainty in risk. Various two-stage methods have been proposed that first estimate a correlation structure and then generate Monte Carlo simulations, which incorporate this structure while leaving marginal distributions of parameters unchanged. Here we propose a one-stage alternative, in which the correlation structure is estimated from the data directly by Bayesian Markov Chain Monte Carlo methods. Samples from the posterior distribution of the outputs then correctly reflect the correlation between parameters, given the data and the model. Besides its computational simplicity, this approach utilizes the available evidence from a wide variety of structures, including incomplete data and correlated and uncorrelated repeat observations. The major advantage of a Bayesian approach is that, rather than assuming the correlation structure is fixed and known, it captures the joint uncertainty induced by the data in all parameters, including variances and covariances, and correctly propagates this through the decision or risk model. These features are illustrated with examples on emissions of dioxin congeners from solid waste incinerators.

Journal Article↗
PubMed2003

Simulating bioremediation of uranium-contaminated aquifers; uncertainty assessment of model parameters.

Bioremediation of trace metals and radionuclides in groundwater may require the manipulation of redox conditions via the injection of a carbon source. For example, after nitrate has been reduced, soluble U(VI) can be reduced simultaneously with other electron acceptors such as Fe(III) or sulfate to U(IV), which may precipitate as a solid (uraninite). To simulate the numerous biogeochemical processes that will occur during the bioremediation of trace-metal-contaminated aquifers, a time-dependent one-dimensional reactive transport model has been developed. The model consists of a set of coupled mass balance equations, accounting for advection, hydrodynamic dispersion, and a kinetic formulation of the biological or chemical transformations affecting an organic substrate, electron acceptors, corresponding reduced species, and trace metal contaminants of interest, uranium in this study. This set of equations is solved numerically, using a finite difference approximation. The redox conditions of the domain are characterized by estimating the pE, based on the concentration of the dominant terminal electron acceptor and its corresponding reduced species. This pE and the concentrations of relevant species are then used by a modified version of MINTEQA2, which calculates the speciation/sorption and precipitation/dissolution of the species of interest under equilibrium conditions. Kinetics of precipitation/dissolution processes are described as being proportional to the difference between the actual and calculated equilibrium concentration. A global uncertainty assessment, determined by Random Sampling High Dimensional Model Representation (RS-HDMR), was performed to attain a phenomenological understanding of the origins of output variability and to suggest input parameter refinements as well as to provide guidance for field experiments to improve the quality of the model predictions. By decomposing the model output variance into its different input contributions, RS-HDMR can identify the model inputs with the most influence on various model outputs, as well as their behavior pattern on the model output. Simulations are performed to illustrate the effect of biostimulation on the fate of uranium in a saturated aquifer, and to identify the key processes that need to be characterized with the highest accuracy prior to designing a uranium bioremediation scheme.

Biodegradation, Environmental↗
PubMed1993

Different ways of modeling spatial-frequency uncertainty in visual signal detection.

Inferior human signal-detection behavior compared with that of ideal observers has been explained by intrinsic uncertainty of the human observer with respect to certain signal parameters. One way to model this uncertainty is to assume that the observer simultaneously monitors multiple channels, corresponding to possible parameters. However, it is also conceivable to assume that an observer, uncertain about which channel to monitor, chooses a suboptimally tuned single filter. Finally, uncertainty may also cause the filter underlying a single channel to broaden. In this paper these different models are investigated with respect to spatial-frequency uncertainty for matched filters detecting Gabor signals. All three mechanisms predict a decrease in detection performance. However, it is shown that the resulting psychometric functions are different. While the slopes increase with uncertainty for the multiple-channel models, they decrease for a randomly chosen single channel. Broadening a single filter leads to parallel psychometric functions.

Humans↗
PubMed2004

Fugacity-based indoor residential pesticide fate model.

Dermal and nondietary pathways are possibly important for exposure to pesticides used in residences. Limited data have been collected on pesticide concentrations in residential air and surfaces following application. Models may be useful for interpreting these data and to make predictions about concentrations in the home for other pesticides based on chemical properties. We present a dynamic mass-balance compartment model based on fugacity principles. The model includes air (both gas phase and aerosols), carpet, smooth flooring, and walls as model compartments. Six size fractions of particulate matter with different fate and transport properties are included. We determine the compartmental fugacity capacity and mass-transfer rate coefficients between compartments. We compare model results to chlorpyrifos air and carpet measurements from an independent study. For a comparison, we run the same simulation for diazinon and permethrin. We quantify the effect of parameter uncertainty and model uncertainties related to the source release rate and conduct a sensitivity analysis to determine which parameters contribute most to output uncertainty. In the model comparison to chlorpyrifos measurements, the model results are of the same order of magnitude as measured values but tend to overpredict the measured data, thus indicating the need for a better understanding of emissions from treated surfaces.

Aerosols↗
PubMed1998

Evaluation (not validation) of quantitative models.

The present regulatory climate has led to increasing demands for scientists to attest to the predictive reliability of numerical simulation models used to help set public policy, a process frequently referred to as model validation. But while model validation may reveal useful information, this paper argues that it is not possible to demonstrate the predictive reliability of any model of a complex natural system in advance of its actual use. All models embed uncertainties, and these uncertainties can and frequently do undermine predictive reliability. In the case of lead in the environment, we may categorize model uncertainties as theoretical, empirical, parametrical, and temporal. Theoretical uncertainties are aspects of the system that are not fully understood, such as the biokinetic pathways of lead metabolism. Empirical uncertainties are aspects of the system that are difficult (or impossible) to measure, such as actual lead ingestion by an individual child. Parametrical uncertainties arise when complexities in the system are simplified to provide manageable model input, such as representing longitudinal lead exposure by cross-sectional measurements. Temporal uncertainties arise from the assumption that systems are stable in time. A model may also be conceptually flawed. The Ptolemaic system of astronomy is a historical example of a model that was empirically adequate but based on a wrong conceptualization. Yet had it been computerized--and had the word then existed--its users would have had every right to call it validated. Thus, rather than talking about strategies for validation, we should be talking about means of evaluation. That is not to say that language alone will solve our problems or that the problems of model evaluation are primarily linguistic. The uncertainties inherent in large, complex models will not go away simply because we change the way we talk about them. But this is precisely the point: calling a model validated does not make it valid. Modelers and policymakers must continue to work toward finding effective ways to evaluate and judge the quality of their models, and to develop appropriate terminology to communicate these judgments to the public whose health and safety may be at stake.

Models, Biological↗
PubMed2006

Estimates of the uncertainties associated with models of the nucleon structure functions in the Delta production region.

Theoretical studies of the inclusive electron-nucleus cross section at beam energies up to a few GeV show that, while the region of the quasielastic peak is understood at the quantitative level, the data in the Delta production region are sizably underestimated. We analyze the uncertainty associated with the description of the nucleon structure functions W1 and W2 and its impact on the nuclear cross section. The results of our study suggest that the failure to reproduce the data is to be mostly ascribed to the poor knowledge of the neutron structure functions at low Q2.

Journal Article↗
PubMed2006

Using mathematical models to assess sediment stability.

The application of mathematical models to a sediment stability study is presented, with an emphasis on using models as a component of an effort to develop, refine, and potentially validate a conceptual site model (CSM) for sediment transport at a study site. The utility of mathematical models is discussed, in which the modeling framework consists of linked hydrodynamic, sediment transport, and contaminant fate and transport models. Benefits and drawbacks of empirically based mechanistic models are presented. An approach for integrating modeling analyses into the development, refinement and validation of a CSM is provided. This approach focuses on a phased study that combines modeling and data-based analyses to test hypotheses related to the CSM and sediment stability. Uncertainty in modeling results is a primary concern in sediment stability studies, and issues related to model uncertainty are discussed. Finally, communication of modeling results to stakeholders is addressed.

Environmental Pollutants↗